Psychology is science.
Of course it is, that's why it doesn't deal with morality, what is right and wrong and why it is so. Philosophy deal with that. You are confused about moral psychology and morality. The former deals with how we choose or what is the cause for acting moral or immoral.
Psychology does not and cannot answer the questions, "is being gay right or wrong? Why or why not?" However, it can answer the questions, "why is someone homophobic? What is the cause for someone to be that way?"
Every route of sin has a story to tell. For example, I always ask myself, "Where do selfish people ends up?" Sometimes, I ask myself, "Where do bullying people end up in their life?" That is still science.
No, that's not science. Those questions are not scientific, philosophical at most. No scientific method cannot be use to for such purpose, that is, being able to replicate and not having it where an infinite amount of variables can effect the research.